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a satellite with a mass of 100kg fires it’s engines to increase velocity, thereby increasing the size of its orbit around the earth. as a result it moves from a circular orbit if radius 7.5x10^6 m to an orbit of radius 7.7x10^6 m. what is the approximate change in gravitational force from the earth as a result of this change in the satellites orbit?

Sagot :

The approximate change in gravitational force from Earth as a result of the change in radius of the satellite's orbit is -95.07N

What is the universal law of gravitation?

The universal law of gravitation states that the particle of matter in the universe attracts another particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

It is written thus;

F = G [tex]M_1M_2[/tex]÷ [tex]r^2[/tex]

Where

F = Gravitational force

G = Gravitational constant

[tex]M_1[/tex] and [tex]M_2[/tex] are the masses of the object

r = radius

How to calculate the gravitational force

Formula:

F = G [tex]M_1M_2[/tex]÷ [tex]r^2[/tex]

Given [tex]M_1[/tex] = 100kg

[tex]M_2[/tex] = 5.97 x[tex]10^{24}[/tex] kg

r = 7.5 x [tex]10^6[/tex] m

G =  6.67 x [tex]10^{-11}[/tex] N-m²/kg²

For the first orbit, substitute the values

F = 6.67 x [tex]10^{-11}[/tex]× 150 ×  5.97 x [tex]10^{24}[/tex] ÷ (7.5 x[tex]10^6[/tex])[tex]^2[/tex]

F = 5.95 × [tex]10^{16}[/tex] ÷ 56.25 × [tex]10^{12}[/tex]=  105.77 N

For the second orbit of radius 7.7 x 10^6 m

F =  6.67 x [tex]10^{-11}[/tex] × 100 ×  5.97 x [tex]10^{24}[/tex] ÷ (7.7 x [tex]10^6[/tex])2

F = 5.95 × [tex]10^{16}[/tex]÷ 59.25 × [tex]10^{12}[/tex] = 200. 84 N

The approximate change = 105. 77 - 200. 84 = -95.07N

Hence, the approximate change in gravitational force from Earth as a result of the change in radius of the satellite's orbit is -95.07N

Learn more about gravitational force here:

brainly.com/question/19050897

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